What are the solutions to the equation p^2-1/3 p-1/2 =0 ?

The solutions to the equation p^2-1/3 p-1/2 =0 are p=(1+sqrt(19))/6 ,p=(1-sqrt(19))/6

Find the zeros of p^2-1/3 p-1/2 =0

The zeros of p^2-1/3 p-1/2 =0 are p=(1+sqrt(19))/6 ,p=(1-sqrt(19))/6

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p^{2} - \frac{1}{3} p - \frac{1}{2} = 0

p = \frac{1 + 19}{6}, p = \frac{1 - 19}{6}

Decimal Notation

p = 0.89314 \dots, p = - 0.55981 \dots

Solution steps

p^{2} - \frac{1}{3} p - \frac{1}{2} = 0

Find Least Common Multiplier of

3, 2 : 6

Multiply by LCM=

6

p^{2} \cdot 6 - \frac{1}{3} p \cdot 6 - \frac{1}{2} \cdot 6 = 0 \cdot 6

Simplify

6 p^{2} - 2 p - 3 = 0

Solve with the quadratic formula

p_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 6 ( - 3 )}{2 \cdot 6}

(- 2)^{2} - 4 \cdot 6 (- 3) = 219

p_{1, 2} = \frac{- ( - 2 ) \pm 2 19}{2 \cdot 6}

Separate the solutions

p_{1} = \frac{- ( - 2 ) + 2 19}{2 \cdot 6}, p_{2} = \frac{- ( - 2 ) - 2 19}{2 \cdot 6}

p = \frac{- ( - 2 ) + 2 19}{2 \cdot 6} : \frac{1 + 19}{6}

p = \frac{- ( - 2 ) - 2 19}{2 \cdot 6} : \frac{1 - 19}{6}

The solutions to the quadratic equation are:

p = \frac{1 + 19}{6}, p = \frac{1 - 19}{6}

6 x^{2} - 6 - 5 x = 0

- 4 z^{2} + 13 z - 3 = 0

u^{2} + 13 u + 36 = 0

- 2 x + 1 = - x^{2} + 4

4 - x^{2} = 2 + x

What are the solutions to the equation p^2-1/3 p-1/2 =0 ?
The solutions to the equation p^2-1/3 p-1/2 =0 are p=(1+sqrt(19))/6 ,p=(1-sqrt(19))/6
Find the zeros of p^2-1/3 p-1/2 =0
The zeros of p^2-1/3 p-1/2 =0 are p=(1+sqrt(19))/6 ,p=(1-sqrt(19))/6